Question

If 3 consecutive positive integers are the angles of a triangle, then find the three angles of the triangle. Show or explain your work.

A) 30°, 60°, 90°
B) 45°, 45°, 90°
C) 36°, 72°, 72°
D) 20°, 40°, 120°.

Answer 1

When three consecutive positive integers are considered as angles of a triangle, the angles are 59°, 60°, and 61°.

Step-by-step explanation:

When considering three consecutive positive integers as angles of a triangle, we know that the sum of the angles of a triangle is always 180 degrees. Let's represent the three consecutive integers as x, x+1, and x+2.

So, x + (x+1) + (x+2) = 180 degrees.

Combining like terms, we have 3x + 3 = 180.

Simplifying the equation, we get 3x = 177, and dividing both sides by 3 gives x = 59.

Therefore, the three angles of the triangle are 59°, 60°, and 61°. So, the correct answer is option (c) 59°, 60°, 61°.